Infinity is a funny little guy, popping up like a weed in all these unexpected places.
Most of us have have likely found ourselves standing or sitting between two mirrors and seeing our image repeated “forever”, as the reflected image reflects itself which in turn is reflected and so on. And on. And on. This is known as an “infinity mirror”, or barbershop mirrors. My buddy Bill and I, back when we worked for the Corps of Engineers, would sometimes encounter these infinite loops caused by the irrational world of government bureaucracy. At such times we would look at each other and gleefully cackle, “Barbershop Mirrors”!
In the Arts there is this type of painting or drawing called a droste image which is an image that contains within it a smaller replica of itself, and so on and so on. The effect is named for a Dutch brand of cocoa first sold in 1904. The advertisement, designed by Jan Missetis, is shown here with a nurse holding a can of “Droste’s Cacao”, which itself contains a smaller image of the can. Why a nurse I can only imagine.
Back to barbershop mirrors. Real images in real mirrors don’t actually go off to infinity because mirrors are not perfect and some light is lost each time the image is reflected. Mathematics contains no such constraints, so the principles of geometric optics applied to the infinity mirror describe a perfect mathematical surface with the wonderful name of Gabriel’s Horn. In theory, the surface of Gabriel’s Horn is infinite in area, but encloses a finite volume. Consider our minds officially blown.
The name Gabriel refers to the Archangel Gabriel who, it is said, blows his horn to announce Judgement Day. The Infinite announces the Finite, which has to be one of the coolest things ever. Who said mathematics was boring?
whoisfenton 